# Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories

@article{Arsiwalla2021HomotopiesIM, title={Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories}, author={Xerxes D. Arsiwalla and Jonathan Gorard and Hatem Elshatlawy}, journal={ArXiv}, year={2021}, volume={abs/2105.10822} }

We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class of rewriting systems, where homotopical maps are induced by the inclusion of appropriate rewriting rules taken from an abstract rulial space of all possible such rules. Furthermore, we show that a multiway rewriting system with homotopies up to order n may…

## One Citation

An Invitation to Higher Arity Science

- Mathematics
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Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the…

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